#include "f2c.h"
#include "blaswrap.h"

/* Table of constant values */

static complex c_b2 = {0.f,0.f};
static integer c__1 = 1;

/* Subroutine */ int chetd2_(char *uplo, integer *n, complex *a, integer *lda, 
	 real *d__, real *e, complex *tau, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;
    real r__1;
    complex q__1, q__2, q__3, q__4;

    /* Local variables */
    integer i__;
    complex taui;
    extern /* Subroutine */ int cher2_(char *, integer *, complex *, complex *
, integer *, complex *, integer *, complex *, integer *);
    complex alpha;
    extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer 
	    *, complex *, integer *);
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int chemv_(char *, integer *, complex *, complex *
, integer *, complex *, integer *, complex *, complex *, integer *
), caxpy_(integer *, complex *, complex *, integer *, 
	    complex *, integer *);
    logical upper;
    extern /* Subroutine */ int clarfg_(integer *, complex *, complex *, 
	    integer *, complex *), xerbla_(char *, integer *);


/*  -- LAPACK routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  CHETD2 reduces a complex Hermitian matrix A to real symmetric */
/*  tridiagonal form T by a unitary similarity transformation: */
/*  Q' * A * Q = T. */

/*  Arguments */
/*  ========= */

/*  UPLO    (input) CHARACTER*1 */
/*          Specifies whether the upper or lower triangular part of the */
/*          Hermitian matrix A is stored: */
/*          = 'U':  Upper triangular */
/*          = 'L':  Lower triangular */

/*  N       (input) INTEGER */
/*          The order of the matrix A.  N >= 0. */

/*  A       (input/output) COMPLEX array, dimension (LDA,N) */
/*          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading */
/*          n-by-n upper triangular part of A contains the upper */
/*          triangular part of the matrix A, and the strictly lower */
/*          triangular part of A is not referenced.  If UPLO = 'L', the */
/*          leading n-by-n lower triangular part of A contains the lower */
/*          triangular part of the matrix A, and the strictly upper */
/*          triangular part of A is not referenced. */
/*          On exit, if UPLO = 'U', the diagonal and first superdiagonal */
/*          of A are overwritten by the corresponding elements of the */
/*          tridiagonal matrix T, and the elements above the first */
/*          superdiagonal, with the array TAU, represent the unitary */
/*          matrix Q as a product of elementary reflectors; if UPLO */
/*          = 'L', the diagonal and first subdiagonal of A are over- */
/*          written by the corresponding elements of the tridiagonal */
/*          matrix T, and the elements below the first subdiagonal, with */
/*          the array TAU, represent the unitary matrix Q as a product */
/*          of elementary reflectors. See Further Details. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A.  LDA >= max(1,N). */

/*  D       (output) REAL array, dimension (N) */
/*          The diagonal elements of the tridiagonal matrix T: */
/*          D(i) = A(i,i). */

/*  E       (output) REAL array, dimension (N-1) */
/*          The off-diagonal elements of the tridiagonal matrix T: */
/*          E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. */

/*  TAU     (output) COMPLEX array, dimension (N-1) */
/*          The scalar factors of the elementary reflectors (see Further */
/*          Details). */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value. */

/*  Further Details */
/*  =============== */

/*  If UPLO = 'U', the matrix Q is represented as a product of elementary */
/*  reflectors */

/*     Q = H(n-1) . . . H(2) H(1). */

/*  Each H(i) has the form */

/*     H(i) = I - tau * v * v' */

/*  where tau is a complex scalar, and v is a complex vector with */
/*  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in */
/*  A(1:i-1,i+1), and tau in TAU(i). */

/*  If UPLO = 'L', the matrix Q is represented as a product of elementary */
/*  reflectors */

/*     Q = H(1) H(2) . . . H(n-1). */

/*  Each H(i) has the form */

/*     H(i) = I - tau * v * v' */

/*  where tau is a complex scalar, and v is a complex vector with */
/*  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), */
/*  and tau in TAU(i). */

/*  The contents of A on exit are illustrated by the following examples */
/*  with n = 5: */

/*  if UPLO = 'U':                       if UPLO = 'L': */

/*    (  d   e   v2  v3  v4 )              (  d                  ) */
/*    (      d   e   v3  v4 )              (  e   d              ) */
/*    (          d   e   v4 )              (  v1  e   d          ) */
/*    (              d   e  )              (  v1  v2  e   d      ) */
/*    (                  d  )              (  v1  v2  v3  e   d  ) */

/*  where d and e denote diagonal and off-diagonal elements of T, and vi */
/*  denotes an element of the vector defining H(i). */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --d__;
    --e;
    --tau;

    /* Function Body */
    *info = 0;
    upper = lsame_(uplo, "U");
    if (! upper && ! lsame_(uplo, "L")) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*lda < max(1,*n)) {
	*info = -4;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("CHETD2", &i__1);
	return 0;
    }

/*     Quick return if possible */

    if (*n <= 0) {
	return 0;
    }

    if (upper) {

/*        Reduce the upper triangle of A */

	i__1 = *n + *n * a_dim1;
	i__2 = *n + *n * a_dim1;
	r__1 = a[i__2].r;
	a[i__1].r = r__1, a[i__1].i = 0.f;
	for (i__ = *n - 1; i__ >= 1; --i__) {

/*           Generate elementary reflector H(i) = I - tau * v * v' */
/*           to annihilate A(1:i-1,i+1) */

	    i__1 = i__ + (i__ + 1) * a_dim1;
	    alpha.r = a[i__1].r, alpha.i = a[i__1].i;
	    clarfg_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &taui);
	    i__1 = i__;
	    e[i__1] = alpha.r;

	    if (taui.r != 0.f || taui.i != 0.f) {

/*              Apply H(i) from both sides to A(1:i,1:i) */

		i__1 = i__ + (i__ + 1) * a_dim1;
		a[i__1].r = 1.f, a[i__1].i = 0.f;

/*              Compute  x := tau * A * v  storing x in TAU(1:i) */

		chemv_(uplo, &i__, &taui, &a[a_offset], lda, &a[(i__ + 1) * 
			a_dim1 + 1], &c__1, &c_b2, &tau[1], &c__1);

/*              Compute  w := x - 1/2 * tau * (x'*v) * v */

		q__3.r = -.5f, q__3.i = -0.f;
		q__2.r = q__3.r * taui.r - q__3.i * taui.i, q__2.i = q__3.r * 
			taui.i + q__3.i * taui.r;
		cdotc_(&q__4, &i__, &tau[1], &c__1, &a[(i__ + 1) * a_dim1 + 1]
, &c__1);
		q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r * 
			q__4.i + q__2.i * q__4.r;
		alpha.r = q__1.r, alpha.i = q__1.i;
		caxpy_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[
			1], &c__1);

/*              Apply the transformation as a rank-2 update: */
/*                 A := A - v * w' - w * v' */

		q__1.r = -1.f, q__1.i = -0.f;
		cher2_(uplo, &i__, &q__1, &a[(i__ + 1) * a_dim1 + 1], &c__1, &
			tau[1], &c__1, &a[a_offset], lda);

	    } else {
		i__1 = i__ + i__ * a_dim1;
		i__2 = i__ + i__ * a_dim1;
		r__1 = a[i__2].r;
		a[i__1].r = r__1, a[i__1].i = 0.f;
	    }
	    i__1 = i__ + (i__ + 1) * a_dim1;
	    i__2 = i__;
	    a[i__1].r = e[i__2], a[i__1].i = 0.f;
	    i__1 = i__ + 1;
	    i__2 = i__ + 1 + (i__ + 1) * a_dim1;
	    d__[i__1] = a[i__2].r;
	    i__1 = i__;
	    tau[i__1].r = taui.r, tau[i__1].i = taui.i;
/* L10: */
	}
	i__1 = a_dim1 + 1;
	d__[1] = a[i__1].r;
    } else {

/*        Reduce the lower triangle of A */

	i__1 = a_dim1 + 1;
	i__2 = a_dim1 + 1;
	r__1 = a[i__2].r;
	a[i__1].r = r__1, a[i__1].i = 0.f;
	i__1 = *n - 1;
	for (i__ = 1; i__ <= i__1; ++i__) {

/*           Generate elementary reflector H(i) = I - tau * v * v' */
/*           to annihilate A(i+2:n,i) */

	    i__2 = i__ + 1 + i__ * a_dim1;
	    alpha.r = a[i__2].r, alpha.i = a[i__2].i;
	    i__2 = *n - i__;
/* Computing MIN */
	    i__3 = i__ + 2;
	    clarfg_(&i__2, &alpha, &a[min(i__3, *n)+ i__ * a_dim1], &c__1, &
		    taui);
	    i__2 = i__;
	    e[i__2] = alpha.r;

	    if (taui.r != 0.f || taui.i != 0.f) {

/*              Apply H(i) from both sides to A(i+1:n,i+1:n) */

		i__2 = i__ + 1 + i__ * a_dim1;
		a[i__2].r = 1.f, a[i__2].i = 0.f;

/*              Compute  x := tau * A * v  storing y in TAU(i:n-1) */

		i__2 = *n - i__;
		chemv_(uplo, &i__2, &taui, &a[i__ + 1 + (i__ + 1) * a_dim1], 
			lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b2, &tau[
			i__], &c__1);

/*              Compute  w := x - 1/2 * tau * (x'*v) * v */

		q__3.r = -.5f, q__3.i = -0.f;
		q__2.r = q__3.r * taui.r - q__3.i * taui.i, q__2.i = q__3.r * 
			taui.i + q__3.i * taui.r;
		i__2 = *n - i__;
		cdotc_(&q__4, &i__2, &tau[i__], &c__1, &a[i__ + 1 + i__ * 
			a_dim1], &c__1);
		q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r * 
			q__4.i + q__2.i * q__4.r;
		alpha.r = q__1.r, alpha.i = q__1.i;
		i__2 = *n - i__;
		caxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[
			i__], &c__1);

/*              Apply the transformation as a rank-2 update: */
/*                 A := A - v * w' - w * v' */

		i__2 = *n - i__;
		q__1.r = -1.f, q__1.i = -0.f;
		cher2_(uplo, &i__2, &q__1, &a[i__ + 1 + i__ * a_dim1], &c__1, 
			&tau[i__], &c__1, &a[i__ + 1 + (i__ + 1) * a_dim1], 
			lda);

	    } else {
		i__2 = i__ + 1 + (i__ + 1) * a_dim1;
		i__3 = i__ + 1 + (i__ + 1) * a_dim1;
		r__1 = a[i__3].r;
		a[i__2].r = r__1, a[i__2].i = 0.f;
	    }
	    i__2 = i__ + 1 + i__ * a_dim1;
	    i__3 = i__;
	    a[i__2].r = e[i__3], a[i__2].i = 0.f;
	    i__2 = i__;
	    i__3 = i__ + i__ * a_dim1;
	    d__[i__2] = a[i__3].r;
	    i__2 = i__;
	    tau[i__2].r = taui.r, tau[i__2].i = taui.i;
/* L20: */
	}
	i__1 = *n;
	i__2 = *n + *n * a_dim1;
	d__[i__1] = a[i__2].r;
    }

    return 0;

/*     End of CHETD2 */

} /* chetd2_ */
